%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET199+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:09:37 PM UTC 2026
% Result : Theorem 1.63s 0.69s
% Output : CNFRefutation 1.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 3
% Syntax : Number of formulae : 45 ( 5 unt; 0 def)
% Number of atoms : 138 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 161 ( 68 ~; 68 |; 18 &)
% ( 5 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 74 ( 66 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,A,B] :
( member(X,intersection(A,B))
<=> ( member(X,B)
& member(X,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,conjecture,
! [A,X,Y] :
( ( subset(A,Y)
& subset(A,X) )
<=> subset(A,intersection(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ! [A,X,Y] :
( ( subset(A,Y)
& subset(A,X) )
<=> subset(A,intersection(X,Y)) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,B)
| ~ member(X,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f15,plain,
! [A,B] :
( ( ? [X] :
( ~ member(X,B)
& member(X,A) )
| subset(A,B) )
& ( ! [X] :
( member(X,B)
| ~ member(X,A) )
| ~ subset(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f14]) ).
fof(f16,plain,
( ! [A,B] :
( ? [X] :
( ~ member(X,B)
& member(X,A) )
| subset(A,B) )
& ! [A,B] :
( ! [X] :
( member(X,B)
| ~ member(X,A) )
| ~ subset(A,B) ) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f17,plain,
( ! [A,B] :
( ( ~ member(sK0_skl(B,A),B)
& member(sK0_skl(B,A),A) )
| subset(A,B) )
& ! [A,B] :
( ! [X] :
( member(X,B)
| ~ member(X,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X,sK0_skl(B,A))],[f16]) ).
fof(f18,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( member(sK0_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f20,plain,
! [X0,X1] :
( ~ member(sK0_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f30,plain,
! [X,A,B] :
( ( ~ member(X,B)
| ~ member(X,A)
| member(X,intersection(A,B)) )
& ( ( member(X,B)
& member(X,A) )
| ~ member(X,intersection(A,B)) ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f31,plain,
( ! [X,A,B] :
( ~ member(X,B)
| ~ member(X,A)
| member(X,intersection(A,B)) )
& ! [X,A,B] :
( ( member(X,B)
& member(X,A) )
| ~ member(X,intersection(A,B)) ) ),
inference(miniscoping,[status(thm)],[f30]) ).
fof(f32,plain,
! [X0,X1,X2] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f33,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f68,plain,
? [A,X,Y] :
( ( subset(A,Y)
& subset(A,X) )
<~> subset(A,intersection(X,Y)) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f69,plain,
? [A,X,Y] :
( ( ~ subset(A,intersection(X,Y))
| ~ subset(A,Y)
| ~ subset(A,X) )
& ( subset(A,intersection(X,Y))
| ( subset(A,Y)
& subset(A,X) ) ) ),
inference(NNF_transformation,[status(thm)],[f68]) ).
fof(f70,plain,
( ( ~ subset(sK3_skl,intersection(sK4_skl,sK5_skl))
| ~ subset(sK3_skl,sK5_skl)
| ~ subset(sK3_skl,sK4_skl) )
& ( subset(sK3_skl,intersection(sK4_skl,sK5_skl))
| ( subset(sK3_skl,sK5_skl)
& subset(sK3_skl,sK4_skl) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl,sK5_skl]),skolemize(A,sK3_skl),skolemize(X,sK4_skl),skolemize(Y,sK5_skl)],[f69]) ).
fof(f71,plain,
( subset(sK3_skl,intersection(sK4_skl,sK5_skl))
| subset(sK3_skl,sK4_skl) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f72,plain,
( subset(sK3_skl,intersection(sK4_skl,sK5_skl))
| subset(sK3_skl,sK5_skl) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f73,plain,
( ~ subset(sK3_skl,intersection(sK4_skl,sK5_skl))
| ~ subset(sK3_skl,sK5_skl)
| ~ subset(sK3_skl,sK4_skl) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f77,plain,
! [X0] :
( subset(sK3_skl,sK5_skl)
| member(X0,intersection(sK4_skl,sK5_skl))
| ~ member(X0,sK3_skl) ),
inference(resolution,[status(thm)],[f18,f72]) ).
fof(f86,plain,
! [X0,X1,X2] :
( ~ member(sK0_skl(intersection(X1,X2),X0),X2)
| ~ member(sK0_skl(intersection(X1,X2),X0),X1)
| subset(X0,intersection(X1,X2)) ),
inference(resolution,[status(thm)],[f20,f34]) ).
fof(f90,plain,
! [X0,X1] :
( member(X1,sK5_skl)
| ~ member(X1,sK3_skl)
| member(X0,intersection(sK4_skl,sK5_skl))
| ~ member(X0,sK3_skl) ),
inference(resolution,[status(thm)],[f77,f18]) ).
fof(f94,plain,
( ~ subset(sK3_skl,sK5_skl)
| ~ subset(sK3_skl,sK4_skl)
| ~ member(sK0_skl(intersection(sK4_skl,sK5_skl),sK3_skl),sK5_skl)
| ~ member(sK0_skl(intersection(sK4_skl,sK5_skl),sK3_skl),sK4_skl) ),
inference(resolution,[status(thm)],[f86,f73]) ).
fof(f97,plain,
! [X0,X1] :
( member(X0,sK5_skl)
| member(X1,sK5_skl)
| ~ member(X1,sK3_skl)
| ~ member(X0,sK3_skl) ),
inference(resolution,[status(thm)],[f90,f33]) ).
fof(f135,plain,
( ~ subset(sK3_skl,sK5_skl)
| ~ subset(sK3_skl,sK4_skl)
| ~ member(sK0_skl(intersection(sK4_skl,sK5_skl),sK3_skl),sK4_skl)
| ~ member(sK0_skl(intersection(sK4_skl,sK5_skl),sK3_skl),sK3_skl)
| ~ member(sK0_skl(intersection(sK4_skl,sK5_skl),sK3_skl),sK3_skl) ),
inference(resolution,[status(thm)],[f97,f94]) ).
fof(f137,plain,
! [X0] :
( subset(X0,sK5_skl)
| ~ member(sK0_skl(sK5_skl,X0),sK3_skl)
| ~ member(sK0_skl(sK5_skl,X0),sK3_skl) ),
inference(resolution,[status(thm)],[f97,f20]) ).
fof(f142,plain,
( ~ subset(sK3_skl,sK5_skl)
| ~ subset(sK3_skl,sK4_skl)
| ~ member(sK0_skl(intersection(sK4_skl,sK5_skl),sK3_skl),sK4_skl)
| ~ member(sK0_skl(intersection(sK4_skl,sK5_skl),sK3_skl),sK3_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f135]) ).
fof(f143,plain,
( ~ subset(sK3_skl,sK5_skl)
| ~ subset(sK3_skl,sK4_skl)
| ~ member(sK0_skl(intersection(sK4_skl,sK5_skl),sK3_skl),sK3_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f142,f18]) ).
fof(f144,plain,
! [X0] :
( subset(X0,sK5_skl)
| ~ member(sK0_skl(sK5_skl,X0),sK3_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f137]) ).
fof(f148,plain,
( subset(sK3_skl,intersection(sK4_skl,sK5_skl))
| ~ subset(sK3_skl,sK5_skl)
| ~ subset(sK3_skl,sK4_skl) ),
inference(resolution,[status(thm)],[f143,f19]) ).
fof(f149,plain,
subset(sK3_skl,intersection(sK4_skl,sK5_skl)),
inference(backward_subsumption_resolution,[status(thm)],[f72,f151]) ).
fof(f150,plain,
( ~ subset(sK3_skl,sK5_skl)
| ~ subset(sK3_skl,sK4_skl) ),
inference(backward_subsumption_resolution,[status(thm)],[f73,f151]) ).
fof(f151,plain,
( subset(sK3_skl,intersection(sK4_skl,sK5_skl))
| ~ subset(sK3_skl,sK5_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f148,f71]) ).
fof(f153,plain,
! [X0] :
( member(X0,intersection(sK4_skl,sK5_skl))
| ~ member(X0,sK3_skl) ),
inference(resolution,[status(thm)],[f149,f18]) ).
fof(f158,plain,
! [X0] :
( member(X0,sK4_skl)
| ~ member(X0,sK3_skl) ),
inference(resolution,[status(thm)],[f153,f32]) ).
fof(f161,plain,
! [X0] :
( subset(X0,sK4_skl)
| ~ member(sK0_skl(sK4_skl,X0),sK3_skl) ),
inference(resolution,[status(thm)],[f158,f20]) ).
fof(f165,plain,
( subset(sK3_skl,sK5_skl)
| subset(sK3_skl,sK5_skl) ),
inference(resolution,[status(thm)],[f144,f19]) ).
fof(f166,plain,
~ subset(sK3_skl,sK4_skl),
inference(backward_subsumption_resolution,[status(thm)],[f150,f167]) ).
fof(f167,plain,
subset(sK3_skl,sK5_skl),
inference(duplicate_literals_removal,[status(thm)],[f165]) ).
fof(f260,plain,
( subset(sK3_skl,sK4_skl)
| subset(sK3_skl,sK4_skl) ),
inference(resolution,[status(thm)],[f161,f19]) ).
fof(f261,plain,
subset(sK3_skl,sK4_skl),
inference(duplicate_literals_removal,[status(thm)],[f260]) ).
fof(f262,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f261,f166]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET199+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n001.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 05:05:43 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 1.63/0.69 % Refutation found
% 1.63/0.69 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.63/0.69 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.63/0.72 % Elapsed time: 0.344255 seconds
% 1.63/0.72 % CPU time: 2.405285 seconds
% 1.63/0.72 % Total memory used: 111.410 MB
% 1.63/0.72 % Net memory used: 106.178 MB
%------------------------------------------------------------------------------